A Pulsar Timing Array Network: Pulsar Count, Timing Precision and Span Required for a Stated Nanohertz Background Amplitude

A pulsar timing array is designed backwards from a target: the smallest nanohertz gravitational-wave background amplitude it must detect. With 68 millisecond pulsars timed to 80 ns root-mean-square every 14 days for 20 years (522 observations per pulsar), the computed detectable characteristic-strain amplitude at a reference frequency of one per year is 6.80e-16. The array's sensitivity improves steeply with span — a factor 4.5 in signal-to-noise against a 10-year programme — and only with the square roots of pulsar count and timing precision, as the accompanying scan quantifies. The dedicated infrastructure is modest: 85 tonnes and 320 kW, because the detectors are the pulsars themselves and the telescopes already exist. All figures are computed from the stated scaling model; the design is simulated, not measured.